Page 30 - Instant notes

A4
LIQUIDS

Key Notes
Liquids have a limited degree of short-range order, but virtually
no long-range order, and are most adequately described in terms
of a radial distribution function—the probability of finding a
neighbor at a given radial distance. The radial distribution
function displays a temperature dependence which correlates with
the effects of temperature on the structure. Generally, increasing
temperature increases the radial distance of the peaks in the radial
distribution function, corresponding to the thermal expansion of
the liquid. The peak intensities also become reduced, as
increasing temperature leads to a more chaotic and dynamic
liquid structure.
Viscosity characterizes the motion of fluids in the presence of a
mechanical shear force. A fluid passing through a capilliary
experiences a retarding force from the walls of the tube, resulting
in a higher velocity along the central axis than at the walls. For
any given small bore capilliary, it is found that a specified
volume of fluid, of density, ρ, flows through the capilliary in a

time, t, given by the .
It is convenient to define a quantity known as the frictional
coefficient, f, which is directly related to molecular shapes
through Stoke’s law. In the ideal case of spherical particles this
may be expressed simply as f=6πηr.
The tendency of a solute to spread evenly throughout the solvent
in a series of small, random jumps is known as diffusion. The
fundamental law of diffusion is Fick’s first law. In the ideal case
of diffusion in one dimension, the rate of diffusion of dn moles of
solute, dn/dt, across a plane of area A, is proportional to the
diffusion coefficient, D, and the negative of the concentration
gradient, −dc/dx:

dn/dt=−DA dc/dx
The diffusion coefficient for a spherical molecule, of radius r, is
related to the viscosity of the solvent through D=kT/(6πηr). If it is
assumed that the molecule makes random steps, then D also
2
allows calculation of the mean square distance, x , over which a
molecule diffuses in a time, t, by the relation .